Lots of anime characters like anime. Virtually any character who is forced to stay at home for whatever reason (Kurenai, Kannagi, etc.) will usually like some anime or another. And really, most of the anime characters are Japanese! While not many are exactly fans, most people over there enjoy at least one or two series....

A lot of characters in anime actually watch anime. There is Satou's neighbor in Welcome to the NHK, Konata Izumi from Lucky Star, Takumi from Chaos Head, that one guy in this mecha anime, Nagi from Hayate, Haruka from Nogizaka Haruka no Himitsu (or something), and pretty much the whole cast from Genshiken,